Related papers: Dynamics of domain wall networks with junctions
We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We…
In this paper we constructed a semi-realistic cosmological model in a dynamic domain wall framework. Our universe is considered to be a (3+1) dimensional dynamic domain wall in a higher dimensional Einstein-Maxwell-Born-Infeld background.…
We study multiplicities and junctions of BPS domain walls interpolating between different chiral vacua in $\mathcal{N}=1$ supersymmetric QCD (SQCD) with the SU$(N)$ gauge group and a varying number of fundamental quarks. Depending on the…
This study offers a detailed analysis of domain wall formation and its cosmological consequences in Einstein-Gauss-Bonnet gravity coupled to a scalar field. A central aspect of the model is the scalar field Lagrangian's ability to…
In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase…
We report on an extensive study of the evolution of domain wall networks in Friedmann-Lema\^{\i}tre-Robertson-Walker universes by means of the largest currently available field-theory simulations. These simulations were done in $4096^3$…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
We study and compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with magnetic filling factors f=1/3 and f=2/5. In addition to the spin waves, the low energy excitations of the system consist…
In this paper we develop a common theoretical framework for the dynamics of thin featureless interfaces. We explicitly demonstrate that the same phase field and velocity dependent one-scale models characterizing the dynamics of relativistic…
We consider the Grand Unified SU(5) model with a small or vanishing cubic term in the adjoint scalar field in the potential. This gives the model an approximate or exact Z$_2$ symmetry whose breaking leads to domain walls. The simplest…
Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often…
The Sznajd cellular automata corresponds to one of the simplest and yet most interesting models of complex systems. While the traditional two-dimensional Sznajd model tends to a consensus state (pro or cons), the assignment of the contrary…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
We consider domain walls embedded in curved backgrounds as an approximation for braneworld scenarios. We give a large class of new exact solutions, exhausting the possibilities for describing one and two walls for the cases where the…
Recent progress has enabled the controlled fabrication of domain walls (DWs) in graphene, which host topological kink states. Meanwhile, reliable techniques for constructing graphene-based Josephson junctions have been established. While…
In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…
A family of degenerate domain wall configurations, partially preserving supersymmetry, is discussed in a generalized Wess-Zumino model with two scalar superfields. We establish some general features inherent to the models with continuously…
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the network does not diverge. In theoretical neuroscience,…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume…